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Volume 21, Issue 12, 01 December 1953

The Temperature Dependence of the Mutual Diffusion Coefficient for Four Gaseous Systems
View Description Hide DescriptionDiffusion coefficients have been measured for the systems He—A, H_{2}—A, H_{2}—nC_{4}H_{10}, and H_{2}–SF_{6} over the temperature range 13°C to 150°C. The values were determined by a point concentration analysis, while diffusion proceeded at one end of a Loschmidt‐type cell. The analysis was made with a hot‐wire technique and utilized the large difference in thermal conductivity to indicate concentration. The generalized equations for calculating D from an experiment with a Loschmidt‐type cell are given as well as an analysis of the errors involved in calculating D from these data.
The data were used to calculate binary force constants for the Lennard‐Jones 6–12 potential. In the system SF_{6}–H_{2} these are ε/k=320°K and (r _{0})_{12}=3.25A. The other three systems fit the theory very poorly. The middle temperature value was about 5 percent low relative to the theoretical curve through the high and low data point. The difficulties of calculating Lennard‐Jones force constants from experimental viscosity or diffusion data are discussed.

Theory of Intermolecular Potential and Second Virial Coefficient of Hydrogen at Low Temperature
View Description Hide DescriptionThe intermolecular potential between hydrogen molecules is calculated taking into account its dependence on the relative orientation of the molecules. Assuming that the rotational quantum number of each molecule is a good quantum number throughout collision at low temperature, the matrix elements of the repulsive short‐range intermolecular potential and the London potential are calculated. If the intermolecular potential depends on the relative orientation of colliding molecules, the resulting matrix element depends on the rotational quantum number. Thus it is pointed out that the second virial coefficient of ordinary hydrogen (which is, at low temperature, a mixture of 75 percent of J = 1 molecule and 25 percent of J = 0 molecules, where J is the rotational quantum number), and pure para hydrogen (which consists of only J = 0 molecules at low temperature) must be different, even if there were no statistical effect. The virial coefficient is calculated for very low temperature by solving the Schrödinger equation numerically.

Nuclear Magnetic Resonance in Metals. II. Temperature Dependence of the Resonance Shifts
View Description Hide DescriptionThe temperature dependence of the nuclear resonance shift in metals has been investigated in lithium,sodium,rubidium, cesium, and gallium. The resonance shifts were found to change by no more than 5 to 6 percent over temperature ranges of 200°, including the melting point. For sodium, the observed temperature dependence of the resonance shift is correlated directly with the volume dependence predicted theoretically for the mass magnetic susceptibility due to the conduction electrons. In the other metals, effects appear which are related apparently to the volume dependence of the wave functions for electrons at the top of the conduction band. The room temperature resonance shifts of Sn^{117} and Sn^{119} and the temperature dependence of the Rb^{87} line width are also reported for the metals. The resonance shift of tin is 0.705×10^{−2}. The estimation of activation energies for self‐diffusion from the temperature dependence of the line widths is discussed.

Fractionation of the Carbon Isotopes in Decarboxylation Reactions. VI. Comparison of the Intermolecular Isotope Effects of a Pair of Isotopic Isomers
View Description Hide DescriptionTheoretical considerations show that malonic acid −2C^{14} should decarboxylate precisely twice as fast as the isotopic isomer malonic acid −1C^{14} liberates C^{14}O_{2}. The calculations are supported by the experimental data of Ropp and Raaen. It is shown that these experiments are consistent with a C^{14}isotope effect twice that of the C^{13} one.

The Proton Magnetic Resonance in Natural Rubber
View Description Hide DescriptionThe protonmagnetic resonance has been observed in natural rubber from liquid nitrogen temperature to room temperature. The absorption line widths show two regions of change. With rising temperature, the first change in width starts at about 155°K, and we assign it to the onset of CH_{3} group rotation. The second, larger change to a narrow line, starts at about 225°K and is assigned to the onset of segmental motions. The latter change coincides with the second‐order transitions observed in various physical properties and provides a direct confirmation of the cause of the transition. Samples cured 30, 60, and 90 minutes were investigated, and it was found that curing has a larger effect on the line width changes at lower temperature than at higher temperature. The inferred greater effect of curing upon CH_{3} group motions than upon segmental motions suggests that cross linking is not the primary mechanism of vulcanization. Rubber stretched 70 percent was found to have the same resonance absorption as unstretched samples.

Temperature Jump and Velocity of Slip at the Boundary of a Gas
View Description Hide DescriptionApproximate expressions are derived from the kinetic theory for the temperature jump and the velocity of slip occurring at an infinite plane solid surface of constant temperature bounding a gas whose state remains invariant throughout all planes parallel to the surface. These derivations differ from earlier ones in the elimination of an assumption, for which an argument is presented as to its untenability, regarding the distribution of the velocities of the molecules striking the surface. Instead, from the mathematical theory of non‐uniform gases are derived conditions on this distribution sufficient to confine possible values of the temperature jump and slip velocity to within fairly close limits.

Note on the Interaction of Methane and Water Vapor in the Hydrogen‐Oxygen Reaction
View Description Hide DescriptionThe influence of methane on the hydrogen‐oxygen reaction was studied in the region of the second‐explosion limit. The experimental data show that there exists a critical concentration of methane, below which both methane and water vapor produce an identical reduction of the explosion limit. Observations on the course of the slow reaction also show that the accelerating effects of these additives on the rate of combination of hydrogen and oxygen are directly related to one another. It is postulated, on the basis of both the explosion and slow reaction rate data, that methane and water vapor influence the kinetics of the hydrogen‐oxygen reaction by similar processes.

The Application of Jacobians to Statistical Thermodynamics
View Description Hide DescriptionShaw's Jacobian method for calculating thermodynamic derivatives is extended so that any partial second derivative can be expressed in terms of two sets of reference derivatives based on the independent variables (V, T) and (P, T), respectively. A simplified and enlarged table of second‐order Jacobians is given in terms of these reference sets. Methods are developed for obtaining the reference J's explicitly in the cases of greatest importance in statistical thermodynamics, i.e., from A, E, the partition function and the caloric equation PV=sE, permitting any first or second partial derivative to be found as an explicit function of (V, T). These J's are given for the polyatomic ideal and van der Waals gases, black‐body radiation, the general (relativistic and nonrelativistic) quantum gas, and the general degenerate Bose‐Einstein and Fermi‐Dirac gases. Their great usefulness is illustrated, and the possible application of reference Jacobians in evaluating semi‐empirical theories of liquids and gases is noted. Finally, the classical theory of thermodynamic fluctuations is extended using Jacobians. General formulas are derived which give explicitly the total variance, partial variance, and covariance of the fluctuation of any thermodynamic variable from its equilibrium value.

The Molar Activity Coefficients of Electrolytes Predicted from Conductivity Data
View Description Hide DescriptionThe molar activity coefficients of uni‐univalent electrolytes may be predicted on the basis of conductivity data with an accuracy of at least 1 percent up to concentrations of the order of 0.01 M in solvents of dielectric constant as low as 10. The method is based on Bjerrum's theory of ion association,^{1} with the ion pair dissociation constant evaluated from conductivity data.^{4–6} The success of the method depends on the use of expressions for y′, the quasi‐activity coefficient of the dissociated fraction, and for Λ, the equivalent conductivity, which go beyond the limiting law approximations of the interionic attraction theory. Equations (6), (8), (10), (12), and (13) have been developed for this purpose. In solvents of dielectric constant 10–40 the prediction involves no adjustable parameters characteristic of the electrolyte. The equations have been tested by comparing the conductivity‐predictedy values for hydrochloric acid with those determined from emf measurements. To insure the significance of this comparison, new emf data for the cell Pt–H_{2}(g)/HCl AgCl–Ag have been obtained for 82.00 wt percent dioxane (D=10.56) in the concentration range 0.0001–0.01 M.

Electronic Properties of Carbons and of Their Interstitial Bisulfate Compounds
View Description Hide DescriptionThe conductivity of graphite increases when it is oxidized into graphite bisulfate, this being the result of the expulsion of resonance electrons by the negative ions and the resulting creation of excess holes in the π‐band. This study concerns the electronic properties of the bisulfate compounds formed by the oxidation of carbons in sulfuric acid, the range of heat‐treatment of carbons extending from 1400°C (baked carbons) to 3000°C (polycrystalline graphite). The resistivities of all samples thus treated decrease with increase in the degree of oxidation. The rate of decrease in resistance depends upon the heat‐treatment, the rate being increasingly greater for samples treated to higher temperatures. The curve of the Hall constant of unoxidized carbonsversus the heat‐treatment temperature H has a sharp positive peak at about H=2000°C. The curve rapidly drops on either side of the peak, the coefficient becoming negative and exhibiting a minimum around H=1400°C.
The thermoelectric power of all samples studied becomes more positive with oxidation, with maxima appearing for lamellar compounds. The rate of the initial rise is greater for higher heat‐treatment temperatures. The temperature coefficient of resistance depends strongly upon the ion concentration, changing from negative to positive for carbons heat‐treated above 2000°C. On the other hand, the coefficients remain negative and are remarkably independent of ion concentration for carbons treated to temperatures below 2000°C.
The results are in general consistent with the electronic model for carbons proposed by Mrozowski whereby the Fermi level is initially depressed during devolatilization of the hydrocarbon material by the formation of a large number of excess holes (heat‐treatments below 1400°C) and later steadily rises with the growth of the crystallites towards the top of the π band, the growth of the crystal planes resulting also in a steady decrease of the energy gap between the π and conduction bands. The negative Hall coefficient for baked carbons indicates the π band to be so depleted that the Fermi level drops at least partially below the inflection curve. At room temperature the conduction is therefore semi‐metallic in nature for carbons treated to H<2000°C in contrast with cases for which H>2000°C where the number of excess holes is relatively small and the current is carried mainly by the holes and electrons thermally activated into the conduction band.

Diffusional Processes in the Growth of Aerosol Particles. II
View Description Hide DescriptionThe effect of the moving boundary of the growingaerosol particle upon the diffusional processes previously investigated for the special case of sinks with stationary boundaries is now discussed in detail. The zeroth‐order approximation for the flux rate, valid for aerosol and most colloidsystems, is found to be of the same analytic form as that for the stationary boundary case. A growth equation is derived for particles growing in the presence of a plurality of competing sinks which deplete the supersaturation. The growth equation here derived is found to be in satisfactory agreement with experiment in the case of barium sulfate crystals growing in aqueous solution. It is further shown that self‐nucleated sols tend to monodispersity with growth. The effects of additional molecules becoming available for diffusion and of variability of the absorption probability are also discussed and evaluated for the special case of a single particle in the diffusion field.

Note on a Nitrogen Molecule Calculation
View Description Hide DescriptionRecent calculations of the binding energy of the nitrogen molecule carried out by Kopineck are examined by means of molecular orbital calculations. The Hellmann‐Kopineck procedure of omitting certain permutations in a valence bond procedure is investigated. It is concluded that the Kopineck calculation should not be used as an argument favoring the 9.8 ev value for the binding energy (D _{0} ^{0}) of the nitrogen molecule.

Applications of the Free Volume Theory of Binary Mixtures
View Description Hide DescriptionDetailed calculations for the free volume theory of binary mixtures are presented and compared with experimental results. It is found that this theory predicts heats of mixing and volumes of mixing larger in magnitude than the observed values and excess entropies of mixing which are smaller than the experimental results. The theory, however, does predict a volume contraction, a negative excess entropy of mixing and a positive heat of mixing for solutions of carbon tetrachloride and neopentane in qualitative agreement with recent observations.

The Infrared Spectrum and Molecular Constants of Sulfur Dioxide
View Description Hide DescriptionBy means of an infrared prism‐grating spectrometer equipped with a multiple‐path cell, seventeen vibration‐rotation absorption bands of SO_{2} have been observed and recorded. Seven bands exhibiting rotational structure were analyzed for the rotational constants of the upper and lower vibrational states. Harmonic and anharmonic constants in the vibrational energy expression have been calculated, and suitable values for the force constants in a four‐constant potential function have been obtained. No bands ascribable to S^{34}O_{2} ^{16} were found.

Diffusion and Thermal Diffusion of Isotopic Gases
View Description Hide DescriptionThe thermal diffusion ratio, R_{T} , for argon and neon isotopes is known to be a linear function of lnT over a considerable temperature range. It is shown that d lnD/d lnT must also be approximately linear in lnT, and that the diffusion coefficient, D, should therefore obey an empirical equation of the formwhere α, β, γ are constants. Considerable latitude is possible in the values of these constants which can reproduce the diffusion data available at the present time. Satisfactory values of β and γ can be found from thermal diffusion data. Except for the factor α, D(T) can thus be calculated from R_{T} (T). It is also possible to calculate the thermal diffusion ratio as a function of temperature from measurements of the diffusion coefficient, but completely reliable results require more extensive diffusion data than is now available.

A Sum Rule for the Vibrational Frequencies of Homologs
View Description Hide DescriptionIt is shown empirically that the zero‐point energy in substituted methanes may be treated as a constitutive property when account is taken of the interaction between nonbonded atoms. Thus, the sum of the vibration frequencies (Σν) of the halogenated methanes is found to have the predicted quadratic dependence on the number of substituents. This reduces to a linear dependence in the case of isotopically substituted homologs, compared to the linear dependence for Σν^{2} found theoretically by Decius and Wilson, and Sverdlov. Both Σν and Σν^{2} give good agreement between observed and calculated results. Various applications are given for the Σν rule and it is shown further that Σν, Σν^{2}, Σ1/ν, Σ1/ν^{2} are all approximately constitutive properties of the halogenated methanes.

The Assignments of the Raman and Infrared Frequencies of 1,2‐Dichloroethane Observed in the Gaseous, Liquid, and Solid States
View Description Hide DescriptionBased on the normal vibration calculation of the trans and the gauche molecules of 1,2‐dichloroethane as an eight‐body problem, the assignments of the Raman and infrared frequencies of this substance observed in the gaseous, liquid, and solid states have been made. The vibrational modes of these frequencies have been discussed.

A Calculation of the Diamagnetic and Paramagnetic Susceptibility of N_{2} by the Statistical Method
View Description Hide DescriptionThe diamagnetic and the paramagnetic term in the susceptibility of N_{2} are calculated using the statistical method of Thomas and Fermi corrected for exchange and correlation effects. A statistical electron density of N_{2}, corrected for exchange and correlation, is used in the evaluation of the integral ∫ ρr ^{2} dv, which defines the mean square position of the electronic charge of the molecule appearing in the diamagnetic term. A statistical distribution function of the square electronic angular momentum of the molecule is derived, and the mean square electronic angular momentum of the molecule, appearing in the paramagnetic term, is defined in terms of the distribution function. This procedure leads to a result which, although approximately two times larger than the observed value, still is fully as good as similar calculations for atoms.

Kinetics of the Fast Reaction between Nitrogen Dioxide and Fluorine
View Description Hide DescriptionThe rate of the reaction between nitrogen dioxide and fluorine to form nitryl fluoride has been measured at 27.7, 50.4, and 70.2°. Light absorption by nitrogen dioxide was used to follow the reaction. By using a 22‐liter Pyrex flask and by going to low concentrations of reactants, between 0.5 and 20×10^{−8} moles cc^{−1}, the rate of this fast reaction was reduced to a convenient value. The rate was found to be first order in each reactant, and it showed no dependence on nitryl fluoride. The proposed mechanism isThe empirical second order rate constant is k _{1}, that of an elementary bimolecular reaction. If the rate constant is written as Ae^{−E/RT } then A is 1.6×10^{12} cc moles^{−1} sec^{−1} and E is 10.5 kcal.

The Entropy of Aqueous Oxy‐Anions
View Description Hide DescriptionThe entropies of oxy‐anions of the formula XO_{ n } ^{−Z } are well represented by the equation S̄ _{2} ^{0}=43.5–46.5 (Z−0.28n). Species containing hydroxyl groups are included by disregarding the hydroxyl groups in counting the number of oxygens n. The form of the equation is partially justified on the basis of a model. Binuclear ions are treated by calculating for the two halves separately and making a correction for the entropy of dimerization.